Question: Solve for $x$ and $y$ using elimination. ${6x+4y = 62}$ ${-5x-5y = -60}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $4$ ${30x+20y = 310}$ $-20x-20y = -240$ Add the top and bottom equations together. $10x = 70$ $\dfrac{10x}{{10}} = \dfrac{70}{{10}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {6x+4y = 62}\thinspace$ to find $y$ ${6}{(7)}{ + 4y = 62}$ $42+4y = 62$ $42{-42} + 4y = 62{-42}$ $4y = 20$ $\dfrac{4y}{{4}} = \dfrac{20}{{4}}$ ${y = 5}$ You can also plug ${x = 7}$ into $\thinspace {-5x-5y = -60}\thinspace$ and get the same answer for $y$ : ${-5}{(7)}{ - 5y = -60}$ ${y = 5}$